A study on Copson operator and its associated sequence space
Hadi Roopaei
Abstract
Abstract In this research, we investigate two types of Copson matrices, the generalized Copson matrix and the Copson matrix of order n , and their associated sequence spaces generated by these matrices. We also investigate the topological properties, inclusions, and dual spaces of these new Banach spaces as well as compute the norm of Copson operators on the well-known matrix domains such as Hilbert and difference sequence spaces. Moreover, in a reverse manner, we investigate the norm of well-known operators on the Copson matrix domains generated with Copson matrices. Through this study we introduce several new inequalities, inclusions, and factorizations for well-known operators.
Topics & Concepts
MathematicsSequence (biology)Sequence spacePure mathematicsHilbert spaceNuclear operatorNorm (philosophy)Operator theoryOperator normMatrix (chemical analysis)Compact operator on Hilbert spaceMatrix normBanach spaceAlgebra over a fieldDiscrete mathematicsCompact operatorApproximation propertyExtension (predicate logic)Eigenvalues and eigenvectorsComputer sciencePhysicsPolitical scienceQuantum mechanicsBiologyGeneticsProgramming languageMaterials scienceLawComposite materialApproximation Theory and Sequence SpacesMathematical Analysis and Transform MethodsHolomorphic and Operator Theory